Copiaco, Chile (CNN) -- The wife of one of the 33 men trapped 2,300 feet below ground in Chile gave birth Tuesday to a daughter, a relative said.
Elizabeth Segovia, wife of Ariel Ticona, was recovering in a hospital after giving birth to a 4-kilogram (8.8 lbs.), 48-centimeter (19-inch) girl, said Ticona's sister, Veronica Ticona.
The daughter was to have been named Carolina, but that plan was changed after the August 5 cave-in trapped her father, Veronica Ticona said.
Nearly two weeks ago, Segovia got a handwritten letter from her husband -- sent through the 4-inch-wide hole that has served as an umbilical cord to the miners -- proposing they name their daughter Esperanza Elizabeth instead. Esperanza is Spanish for hope.
"First, because we never lost hope; second, because it's the name of the camp where the families are living; and third, because the 33 miners never lost hope either," Segovia said earlier in September.
Esperanza is believed to be the first child born to any of the 33 men since they were trapped.
In the 40 days that have followed, their contact with the outside world has been limited to what rescuers have been able to pass through the narrow hole that reaches into the cave ceiling.
Ticona said her brother was told of the birth by a video conference system. "He is very happy to be a father," she said.
Segovia discovered that their child would be a girl by looking at a grainy ultrasound on August 4, the day before the mine collapse. "My world just collapsed," she said earlier this month. "I couldn't react. I just cried and cried."
But, she added, she forced herself to stop crying because doing so adversely affected her fetus.
The tube to the mine has carried life-affirming news in both directions. A few days after seeing her daughter on grainy, flickering ultrasound images, Segovia saw her husband on grainy video that the miners shot by the flickering lights mounted on their mining helmets, then packed into the tube for the journey upward.
With her daughter's arrival Tuesday, Segovia is now waiting for her husband's arrival in the months ahead.
The couple also have two sons, ages 5 and 9.
CNN's Karl Penhaul contributed to this story.